Background

This document has nls (non-linear least squares) regression fits using the log-normal functional form to USFS FIA (United States Forest Service Forest Inventory & Analysis) biomass growth vs. stand age relationships. This functional form is commonly used in growth analyses, and permits a flexible shape to fit to data in an intermediate maximum (i.e., “hump” shaped) relationship. We use the sum of tree biomass growth increment method for the plot biomass growth (\(G\)) calculation (see supplementary methods). Models are fitted separately by US ecoprovince.

Hypothetically, the entire functional form of the following non-linear model is considered: \(G = (1 + (yr-1990) \cdot ge/100) \times (1 - \alpha \cdot B_l) \times (1 + \phi \cdot \Delta PDSI) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left( StdAge_{t1} /c \right)} {d} \right]} ^2 \right)\), where \(G\) is the plot level biomass growth calculated as the sum of tree biomass growth increments, \(B_l\) is the calculated proportion of biomass loss over the census interval, \(StdAge_{t1}\) is the FIA-estimated stand age at the first of two FIA plot tree censuses, \(\Delta PDSI\) is the difference in the growing season (January-August) annual average PDSI values over the FIA plot measurement intervals and a 30-year climate normal (1969-1990), and \(yr\) is the measurement year (all FIA data). Free parameters are \(\alpha\): the growth compensation of lost plot biomass, \(ge\): biomass growth enhancement over time, \(a\): the y-intercept of the curve, \(a +b\): the peak value of \(G\), \(c\): the \(StdAge_{t1}\) value at peak \(G\), and \(d\): the curve shape parameter.

Data have increasing variance in \(G\) with increasing \(StdAge_{t1}\), Thus, weighted nls is the best approach. We explore a few weighting options and found that proportional weighting can be achieved by weighting observations by \(\frac {1} {meanG}\) in equal-sample sized plot biomass bins (n=20) for each ecoprovince.

Model selection is used to determine. to determine the best fitting models, which is implemented in two parts. A first model selection is done to determine the best model form either including \(\alpha\): the biomass compensation effect due to lost biomass (natural mortality or harvest), \(\phi\): the effect of changing climate (quantified as \(\Delta PDSI\), or both. \(\Delta PDSI\) is defined the difference in the Palmer drought severity index from January - August for the 10 years preceding the biomass measurement and the 1969-1990 period). We explored \(\Delta PDSI\) using only the summer growing months (June-August) over the same intervals, and analyses were insensitive to that change. For the first model selection the following models are considered:

model 1: simple model \(G = (1 + (yr-1990) \cdot ge/100) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left( StdAge_{t1} /c \right)} {d} \right]} ^2 \right)\)

model 2: phi model \(G = (1 + (yr-1990) \cdot ge/100) \times (1 + \phi \cdot \Delta PDSI) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left( StdAge_{t1} /c \right)} {d} \right]} ^2 \right)\)

model 3: phi-alpha model \(G = (1 + (yr-1990) \cdot ge/100) \times (1 + \phi \cdot \Delta PDSI) \times (1 - \alpha \cdot B_l) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left( StdAge_{t1} /c \right)} {d} \right]} ^2 \right)\)

NOTE:

This document contains all \(G\) observations that meet our plot based filtering criteria:

  1. exclude FIA plots in plantation forests
  2. exclude FIA plots with multiple plot conditions (COND_PROG_UNADJ > 0.95)
  3. exclude FIA plots non-productive stands (i.e., those with less than 20 ft^3/acre/year timber producing capability; SITECLCD of 7)
  4. exclude FIA plots in non-stocked stands (i.e., those with STDSZCD of 5)
  5. exclude FIA plots in non-accessible areas (i.e., private lands etc., COND_STATUS_CD not equal to 1)
  6. exclude FIA plot visits that are not part of the annual inventories (which also includes FIA plot visits for Phase 3 ozone measurements)

Additionally, in an effort to clean up the data set, we have removed outlier observations, using a quantile threshold approach. We also calculated plot \(G\) using as biomass balance method (see supplementary methods), and the difference between the two methods. Accordingly, we define \(diff_G\) as the difference between tree incremental \(G\) and biomass balance \(G\). We excluded observations which meet the following criteria using a 0.5% quantile (\(QT\)):

  • case A: where the \(QT\) difference in tree incremental \(G\) is > biomass balance plot G (i.e., > 99.5% \(diff_G\) positive outliers)

  • case B: where the \(QT\) difference in tree incremental \(G\) is < mass balance plot G (i.e., < 0.5% \(diff_G\) negative outliers)

  • case C: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., > 99.5% positive outliers)

  • case D: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., < 0.5% negative outliers)

These data set cleaning criteria resulted in the exclusion of 1677 observations.

Below the model fitting procedure is implemented by ecoprovince:

211 - Northeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq  F value  Pr(>F)    
## 1   6799     5243.9                                
## 2   6798     5240.3  1   3.547   4.6014 0.03198 *  
## 3   6797     4946.6  1 293.714 403.5836 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 25284.27
## 2     2 25281.66
## 3     3 24891.20
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.292872   0.163470   1.792   0.0732 .  
## phi    0.010286   0.004348   2.366   0.0180 *  
## alpha  0.644419   0.030041  21.451   <2e-16 ***
## a     -6.319123  16.323713  -0.387   0.6987    
## b      9.731894  16.313339   0.597   0.5508    
## c     29.516194   1.963439  15.033   <2e-16 ***
## d      4.920382   4.450084   1.106   0.2689    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8531 on 6797 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 7.621e-06
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 1 rows containing missing values (geom_point).

plotting 2

212 - Laurentian Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq  F value    Pr(>F)    
## 1  18726      16075                                  
## 2  18721      16009  5   66.26   15.498 3.029e-15 ***
## 3  18720      14917  1 1091.78 1370.124 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 65771.72
## 2     2 65686.39
## 3     3 64365.59
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.885982   0.141057   6.281 3.44e-10 ***
## phi    0.025852   0.002867   9.018  < 2e-16 ***
## alpha  0.827263   0.020518  40.319  < 2e-16 ***
## a      0.722858   0.373130   1.937   0.0527 .  
## b      1.832104   0.365116   5.018 5.27e-07 ***
## c     19.734593   0.815916  24.187  < 2e-16 ***
## d      2.337867   0.345363   6.769 1.33e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8927 on 18720 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 2.592e-06
##   (48 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 23 rows containing missing values (geom_point).

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_221$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_221.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

## Error in nls(fg2_1, data = G_222, start = c(ge = ge.start, a = a.start,  : 
##   singular gradient
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_222$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_222.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   8769     9241.0                                 
## 2   8768     9226.3  1  14.662  13.933 0.0001906 ***
## 3   8764     9007.0  4 219.303  53.346 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 35056.50
## 2     2 35044.56
## 3     3 34826.34
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -1.129281   0.098622 -11.451  < 2e-16 ***
## phi   -0.022440   0.005652  -3.970 7.25e-05 ***
## alpha  0.584152   0.038447  15.194  < 2e-16 ***
## a      2.669375   0.482960   5.527 3.35e-08 ***
## b      1.970422   0.471662   4.178 2.97e-05 ***
## c     29.057795   1.872699  15.517  < 2e-16 ***
## d      1.426937   0.289803   4.924 8.64e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.014 on 8764 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 2.379e-06
##   (12 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 5 rows containing missing values (geom_point).

plotting 2

231 - Southeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq  F value Pr(>F)    
## 1  12311      21643                              
## 2  12310      21640  1    2.8    1.591 0.2072    
## 3  12309      19118  1 2522.2 1623.870 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 60187.33
## 2     2 60187.74
## 3     3 58663.54
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge    -0.0986057  0.0991469  -0.995    0.320    
## phi    0.0007941  0.0040244   0.197    0.844    
## alpha  0.8567398  0.0191847  44.658   <2e-16 ***
## a      3.2349735  0.2112777  15.311   <2e-16 ***
## b      3.2164895  0.1944758  16.539   <2e-16 ***
## c     18.2273027  0.4124116  44.197   <2e-16 ***
## d      1.3141944  0.0855111  15.369   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.246 on 12309 degrees of freedom
## 
## Number of iterations to convergence: 11 
## Achieved convergence tolerance: 6.922e-06
##   (31 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 14 rows containing missing values (geom_point).

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq   F value    Pr(>F)    
## 1  12395      26336                                   
## 2  12394      26317  1   18.36    8.6448  0.003286 ** 
## 3  12393      23747  1 2570.16 1341.3010 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 61358.26
## 2     2 61351.61
## 3     3 60079.33
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.006466   0.122537   0.053   0.9579    
## phi    0.008872   0.004511   1.967   0.0493 *  
## alpha  0.842963   0.020444  41.232   <2e-16 ***
## a      3.481881   0.118222  29.452   <2e-16 ***
## b      2.594932   0.109338  23.733   <2e-16 ***
## c     16.557370   0.402833  41.102   <2e-16 ***
## d      0.923104   0.049522  18.640   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.384 on 12393 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 8.51e-06
##   (70 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 29 rows containing missing values (geom_point).

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)    
## 1   1255     2849.6                             
## 2   1254     2849.5  1   0.12  0.0529 0.8181    
## 3   1253     2692.6  1 156.84 72.9850 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 6292.826
## 2     2 6294.773
## 3     3 6225.438
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.870346   0.901176   0.966 0.334336    
## phi   -0.009029   0.021670  -0.417 0.677010    
## alpha  0.784819   0.082801   9.478  < 2e-16 ***
## a      3.281058   0.556974   5.891 4.93e-09 ***
## b      1.518118   0.413630   3.670 0.000253 ***
## c     18.156020   2.676847   6.783 1.81e-11 ***
## d      0.782773   0.244040   3.208 0.001373 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.466 on 1253 degrees of freedom
## 
## Number of iterations to convergence: 11 
## Achieved convergence tolerance: 8.926e-06
##   (5 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits ## plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96816, p-value = 5.09e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.1636, p-value = 0.001558
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 3 rows containing missing values (geom_point).

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in nls(fg2_2, data = G_242, start = c(ge = ge.start, phi = phi.start,  : 
##   singular gradient
## Error in nls(fg2_3, data = G_242, start = c(ge = ge.start, phi = phi.start,  : 
##   singular gradient
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_242$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_242.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

251 - Prairie Parkland (Temperate)

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   1784     1637.6                                 
## 2   1783     1633.2  1  4.3616  4.7617   0.02923 *  
## 3   1782     1617.6  1 15.6039 17.1896 3.542e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 6743.615
## 2     2 6740.844
## 3     3 6725.669
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.54768    0.29899  -1.832   0.0671 .  
## phi    0.02158    0.01084   1.992   0.0466 *  
## alpha  0.40164    0.09302   4.318 1.66e-05 ***
## a     -0.12904    5.50243  -0.023   0.9813    
## b      3.43455    5.50316   0.624   0.5326    
## c     29.00246    6.18140   4.692 2.91e-06 ***
## d      3.46196    3.40815   1.016   0.3099    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9528 on 1782 degrees of freedom
## 
## Number of iterations to convergence: 14 
## Achieved convergence tolerance: 6.493e-06
##   (8 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93225, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -9.924, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 4 rows containing missing values (geom_point).

plotting 2

255 - Prairie Parkland (Subtropical)

model selection 1

## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_255$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_255.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

262 - California Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

model selection 1

## Error in nls(fg2_1, data = G_263, start = c(ge = ge.start, a = a.start,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(fg2_2, data = G_263, start = c(ge = ge.start, phi = phi.start,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(fg2_3, data = G_263, start = c(ge = ge.start, phi = phi.start,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_263$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_263.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

313 - Colorado Plateau Semi-Desert

model selection 1

## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_313$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_313.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

315 - Southwest Plateau and Plains Dry Steppe and Shrub

model selection 1

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_315.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

321 - Chihuahuan Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

322 - American Semidesert and Desert

model selection 1

## Error in nls(fg2_1, data = G_322, start = c(ge = ge.start, a = a.start,  : 
##   missing or negative weights not allowed
## Error in nls(fg2_2, data = G_322, start = c(ge = ge.start, phi = phi.start,  : 
##   missing or negative weights not allowed
## Error in nls(fg2_3, data = G_322, start = c(ge = ge.start, phi = phi.start,  : 
##   missing or negative weights not allowed
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_322$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_322.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

331 - Great Plains/Palouse Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

332 - Great Plains Steppe

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

341 - Intermountain Semi-desert & Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

342 - Intermountain Semi-Desert

model selection 1

## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_342.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

411 - Everglades

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6722     4631.1                                
## 2   6721     4611.3  1  19.79  28.851  8.08e-08 ***
## 3   6720     4290.0  1 321.32 503.331 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 24157.98
## 2     2 24131.16
## 3     3 23647.28
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.839969   0.191442   4.388 1.16e-05 ***
## phi    0.017844   0.004027   4.431 9.53e-06 ***
## alpha  0.638474   0.026475  24.116  < 2e-16 ***
## a      2.450566   0.125126  19.585  < 2e-16 ***
## b      0.708020   0.082579   8.574  < 2e-16 ***
## c     27.878887   1.761763  15.824  < 2e-16 ***
## d      0.942137   0.155951   6.041 1.61e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.799 on 6720 degrees of freedom
## 
## Number of iterations to convergence: 11 
## Achieved convergence tolerance: 5.478e-06
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 1 rows containing missing values (geom_point).

plotting 2

M221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq  F value Pr(>F)    
## 1   8028      11387                              
## 2   8027      11381  1   6.68   4.7111   0.03 *  
## 3   8026      11111  1 269.82 194.9038 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 36089.85
## 2     2 36087.14
## 3     3 35896.40
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.408200   0.127552  -3.200  0.00138 ** 
## phi   -0.009929   0.005572  -1.782  0.07478 .  
## alpha  0.726136   0.049523  14.663  < 2e-16 ***
## a      3.204776   0.316637  10.121  < 2e-16 ***
## b      1.983587   0.276232   7.181 7.55e-13 ***
## c     26.015032   1.721337  15.113  < 2e-16 ***
## d      1.219745   0.203133   6.005 2.00e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.177 on 8026 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.777e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 1 rows containing missing values (geom_point).

plotting 2

M223 - Ozark Broadleaf Forest Meadow

model selection 1

## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model     AIC
## 1     1 3510.88
## 2     2      NA
## 3     3      NA
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge   2.4228     1.2810   1.891  0.05892 .  
## a    1.5037     0.2854   5.268 1.73e-07 ***
## b    1.0411     0.3042   3.422  0.00065 ***
## c   25.8961     2.6460   9.787  < 2e-16 ***
## d    0.5208     0.1315   3.961 8.08e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.126 on 877 degrees of freedom
## 
## Number of iterations to convergence: 18 
## Achieved convergence tolerance: 7.76e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.98047, p-value = 1.762e-09
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.1975, p-value = 0.2311
## alternative hypothesis: two.sided

predict and plot

plotting 2

M231 - Ouachita Mixed Forest

model selection 1

## Error in nls(fg2_1, data = G_M231, start = c(ge = ge.start, a = a.start,  : 
##   number of iterations exceeded maximum of 50
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_M231$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_M231.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M242 - Cascade Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)    
## 1   3138     7449.1                             
## 2   3137     7446.7  1   2.39  1.0065 0.3158    
## 3   3132     7043.5  5 403.23 35.8603 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 15644.22
## 2     2 15645.21
## 3     3 15457.14
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -1.091782   0.342038  -3.192  0.00143 ** 
## phi   -0.004369   0.015974  -0.274  0.78446    
## alpha  0.997556   0.068924  14.473  < 2e-16 ***
## a      4.878930   0.466285  10.463  < 2e-16 ***
## b      3.462861   0.526379   6.579 5.54e-11 ***
## c     33.740147   1.345010  25.085  < 2e-16 ***
## d      0.412764   0.049270   8.378  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.5 on 3132 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 7.439e-06
##   (40 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.95864, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -13.648, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 7 rows containing missing values (geom_point).

plotting 2

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq  F value    Pr(>F)    
## 1   1939     3672.5                                 
## 2   1938     3467.6  1 204.88 114.5044 < 2.2e-16 ***
## 3   1929     3346.6  9 121.07   7.7541 2.764e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 8948.829
## 2     2 8839.235
## 3     3 8742.612
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -1.52119    0.30445  -4.997 6.36e-07 ***
## phi    0.18344    0.01370  13.394  < 2e-16 ***
## alpha  0.76789    0.08709   8.817  < 2e-16 ***
## a      3.08729    1.55632   1.984  0.04743 *  
## b      4.49689    1.54267   2.915  0.00360 ** 
## c     35.53892    7.53152   4.719 2.54e-06 ***
## d      1.93337    0.66181   2.921  0.00353 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.317 on 1929 degrees of freedom
## 
## Number of iterations to convergence: 16 
## Achieved convergence tolerance: 2.342e-06
##   (27 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96034, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -2.6402, p-value = 0.008286
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 6 rows containing missing values (geom_point).

plotting 2

M262 - Califormia Coastal Range = Coniferous Forest - Open woodland Shrub Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_M313$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_M313.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_M331$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_M331.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value  Pr(>F)    
## 1   2604     2857.0                               
## 2   2603     2850.5  1   6.585  6.0134 0.01426 *  
## 3   2594     2650.2  9 200.295 21.7833 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 9021.477
## 2     2 9017.457
## 3     3 8812.761
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.65586    0.47035  -1.394  0.16331    
## phi    0.03633    0.01614   2.251  0.02447 *  
## alpha  0.84555    0.05293  15.975  < 2e-16 ***
## a      0.68227    0.94027   0.726  0.46814    
## b      2.02084    0.96660   2.091  0.03665 *  
## c     56.12184    4.44187  12.635  < 2e-16 ***
## d      2.01474    0.67929   2.966  0.00304 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.011 on 2594 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 6.49e-06
##   (48 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.88013, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -6.8595, p-value = 6.912e-12
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 12 rows containing missing values (geom_point).

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Error in nls(fg2_1, data = G_M333, start = c(ge = ge.start, a = a.start,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_M333$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_M333.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M334 - Black Hills Coniferous Forest

model selection 1

## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in nls(fg2_3, data = G_M334, start = c(ge = ge.start, phi = phi.start,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_M334$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_M334.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2


Fitted parameters

Best / selected models by ecoprovince

Code Ecoregion Sel.Mod
211 Northeastern Mixed Forest 3
212 Laurentian Mixed Forest 3
221 Eastern Broadleaf Forest NA
222 Midwest Broadleaf Forest NA
223 Central Interior Broadleaf Forest 3
231 Southeastern Mixed Forest 3
232 Outer Coastal Plain Mixed Forest 3
234 Lower Mississippi Riverine Forest 3
242 Pacific Lowland Mixed Forest NA
251 Prairie Parkland (Temperate) 3
255 Prairie Parkland (Subtropical) NA
261 California Coastal Chaparral Forest and Shrub NA
262 California Dry Steppe NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest NA
313 Colorado Plateau Semi-Desert NA
315 Southwest Plateau and Plains Dry Steppe and Shrub NA
321 Chihuahuan Semi-Desert NA
322 American Semidesert and Desert NA
331 Great Plains/Palouse Dry Steppe NA
332 Great Plains Steppe NA
341 Intermountain Semi-Desert and Desert NA
342 Intermountain Semi-Desert NA
411 Everglades NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow 3
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow 3
M223 Ozark Broadleaf Forest Meadow 1
M231 Ouachita Mixed Forest NA
M242 Cascade Mixed Forest 3
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow 3
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow NA
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow NA
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow 3
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow NA
M334 Black Hills Coniferous Forest NA
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow NA

table by ecoprovince

Code Ecoregion region n.obs n.plots ge ge.2.5 ge.97.5 phi phi.2.5 phi.97.5 alpha alpha.2.5 alpha.97.5 a a.2.5 a.97.5 b b.2.5 b.97.5 c c.2.5 c.97.5 d d.2.5 d.97.5
211 Northeastern Mixed Forest east 6806 2847 0.2928722 -0.0275809 0.6133253 0.0102855 0.0017619 0.0188092 0.6444186 0.5855286 0.7033086 -6.3191225 -38.3187109 25.680466 9.7318944 -22.2473568 41.7111455 29.51619 25.66724 33.36515 4.9203821 -3.8031757 13.6439400
212 Laurentian Mixed Forest east 18775 8891 0.8859822 0.6094972 1.1624673 0.0258523 0.0202335 0.0314711 0.8272635 0.7870466 0.8674804 0.7228585 -0.0085100 1.454227 1.8321037 1.1164438 2.5477637 19.73459 18.13532 21.33386 2.3378675 1.6609244 3.0148105
221 Eastern Broadleaf Forest east 7170 3490 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
222 Midwest Broadleaf Forest east 4877 2401 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
223 Central Interior Broadleaf Forest east 8783 3725 -1.1292810 -1.3226030 -0.9359591 -0.0224402 -0.0335203 -0.0113600 0.5841517 0.5087863 0.6595171 2.6693754 1.7226598 3.616091 1.9704217 1.0458534 2.8949900 29.05780 25.38686 32.72873 1.4269371 0.8588555 1.9950187
231 Southeastern Mixed Forest east 12347 5691 -0.0986057 -0.2929491 0.0957377 0.0007941 -0.0070943 0.0086826 0.8567398 0.8191348 0.8943448 3.2349735 2.8208361 3.649111 3.2164895 2.8352865 3.5976925 18.22730 17.41891 19.03569 1.3141944 1.1465794 1.4818095
232 Outer Coastal Plain Mixed Forest east 12470 6101 0.0064662 -0.2337262 0.2466585 0.0088722 0.0000291 0.0177152 0.8429634 0.8028894 0.8830374 3.4818813 3.2501488 3.713614 2.5949315 2.3806130 2.8092501 16.55737 15.76776 17.34698 0.9231039 0.8260340 1.0201738
234 Lower Mississippi Riverine Forest east 1265 714 0.8703464 -0.8976346 2.6383273 -0.0090288 -0.0515430 0.0334854 0.7848195 0.6223761 0.9472628 3.2810584 2.1883541 4.373763 1.5181181 0.7066343 2.3296020 18.15602 12.90442 23.40762 0.7827729 0.3040002 1.2615457
242 Pacific Lowland Mixed Forest pacific 81 81 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
251 Prairie Parkland (Temperate) east 1797 809 -0.5476846 -1.1340860 0.0387169 0.0215844 0.0003274 0.0428414 0.4016421 0.2191965 0.5840877 -0.1290406 -10.9209373 10.662856 3.4345485 -7.3587801 14.2278772 29.00246 16.87890 41.12601 3.4619597 -3.2224364 10.1463557
255 Prairie Parkland (Subtropical) pacific 663 293 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
261 California Coastal Chaparral Forest and Shrub pacific 24 24 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
262 California Dry Steppe pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest pacific 155 155 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
313 Colorado Plateau Semi-Desert interior west 215 215 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
315 Southwest Plateau and Plains Dry Steppe and Shrub interior west 4 4 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
321 Chihuahuan Semi-Desert interior west 9 9 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
322 American Semidesert and Desert interior west 3 3 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
331 Great Plains/Palouse Dry Steppe interior west 304 240 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
332 Great Plains Steppe interior west 195 106 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
341 Intermountain Semi-Desert and Desert interior west 62 62 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
342 Intermountain Semi-Desert interior west 121 120 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
411 Everglades east 93 61 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow east 6729 2989 0.8399694 0.4646825 1.2152563 0.0178435 0.0099492 0.0257379 0.6384745 0.5865748 0.6903741 2.4505658 2.2052783 2.695853 0.7080204 0.5461401 0.8699006 27.87889 24.42527 31.33250 0.9421365 0.6364232 1.2478498
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow east 8034 3700 -0.4082001 -0.6582347 -0.1581655 -0.0099293 -0.0208518 0.0009931 0.7261363 0.6290585 0.8232142 3.2047759 2.5840854 3.825466 1.9835873 1.4421005 2.5250742 26.01503 22.64076 29.38930 1.2197454 0.8215529 1.6179378
M223 Ozark Broadleaf Forest Meadow east 883 343 2.4227544 -0.0915226 4.9370314 NA NA NA NA NA NA 1.5037012 0.9435126 2.063890 1.0411436 0.4440579 1.6382293 25.89607 20.70279 31.08934 0.5208208 0.2627350 0.7789067
M231 Ouachita Mixed Forest east 988 481 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M242 Cascade Mixed Forest pacific 3179 3176 -1.0917823 -1.7624233 -0.4211414 -0.0043693 -0.0356894 0.0269508 0.9975558 0.8624148 1.1326968 4.8789296 3.9646741 5.793185 3.4628610 2.4307789 4.4949430 33.74015 31.10296 36.37734 0.4127636 0.3161582 0.5093689
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow pacific 1963 1963 -1.5211913 -2.1182783 -0.9241044 0.1834450 0.1565842 0.2103058 0.7678897 0.5970888 0.9386907 3.0872948 0.0350396 6.139550 4.4968882 1.4714163 7.5223600 35.53892 20.76815 50.30968 1.9333652 0.6354259 3.2313045
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow interior west 19 19 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow interior west 362 362 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow interior west 1711 1711 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 2649 2648 -0.6558624 -1.5781636 0.2664388 0.0363264 0.0046821 0.0679706 0.8455463 0.7417608 0.9493318 0.6822728 -1.1614916 2.526037 2.0208352 0.1254576 3.9162128 56.12184 47.41187 64.83181 2.0147404 0.6827438 3.3467371
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 1675 1675 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M334 Black Hills Coniferous Forest interior west 362 170 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow interior west 213 213 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA

plot ge

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I

map2

## Warning: package 'ggnewscale' was built under R version 4.2.1
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

plot phi (effect of DeltaPDSI)

plot alpha (biomass growth compensation effect)

plot a coefficient

## Warning: Removed 23 rows containing missing values (geom_point).

plot b coefficient

## Warning: Removed 23 rows containing missing values (geom_point).

plot c coefficient

## Warning: Removed 1 rows containing missing values (geom_hline).
## Warning: Removed 23 rows containing missing values (geom_point).

plot d coefficient

## Warning: Removed 23 rows containing missing values (geom_point).

Caclulations - weighted averages

ge (stand biomass growth enhancement factor in % 2000-2021)

##          region weighted.ge
## 1     entire US -0.03960663
## 2       pacific -1.13380170
## 3          east  0.14185716
## 4 interior west -0.22981654

phi (effect of DeltaPDSI)

##          region weighted.phi
## 1     entire US  0.012690540
## 2       pacific  0.060826694
## 3          east  0.006197611
## 4 interior west  0.012728892

alpha (biomass growth compensation effect)

##          region weighted.alpha
## 1     entire US      0.6087266
## 2       pacific      0.8214344
## 3          east      0.6359597
## 4 interior west      0.2962825

Calculations - weighted averages subsetted to 15 ecoprovinces

  • ecoprovince codes: 211, 212, 221, 223, 231, 232, 234, 251, M211, M221, M223, M231, M242, M261, M332

ge

##          region weighted.ge
## 1     entire US  -0.0462044
## 2       pacific  -1.2558084
## 3          east   0.1506365
## 4 interior west  -0.6558624

phi

##          region weighted.phi
## 1     entire US  0.014804563
## 2       pacific  0.067372162
## 3          east  0.006581174
## 4 interior west  0.036326372

alpha

##          region weighted.alpha
## 1     entire US      0.7101298
## 2       pacific      0.9098277
## 3          east      0.6753185
## 4 interior west      0.8455463